Experimental Study of Two-Fluid Eﬀect during Magnetic

Plasma and Fusion Research: Regular Articles Volume 8, 2401130 (2013)

Experimental Study of Two-Fluid Effect during MagneticReconnection in the UTST Merging Experiment∗)

Kotaro YAMASAKI, Shuji KAMIO1), Koichiro TAKEMURA, Qinghong CAO,Takenori G. WATANABE, Hirotomo ITAGAKI, Takuma YAMADA2),

Michiaki INOMOTO and Yasushi ONOThe University of Tokyo, Kashiwa 277-8561, Japan

1)National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan2)Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

(Received 8 December 2012 / Accepted 17 July 2013)

Radial profile of floating potential inside the current sheet was measured for the purpose of investigating thetwo-fluid (Hall) effect during magnetic reconnection in the UTST merging experiment. During magnetic recon-nection, the floating potential drop was formed spontaneously inside the current sheet, forming a steep electricpotential gradient on its both downstream areas. Magnetic probe array measurement indicates that this potentialdrop appears spontaneously when the reconnection rate rapidly increase due to change in current sheet structure.The IDS probe measurement observed outflow almost equal to poloidal Alfven speed in radial direction from theX-point, where steep gradient of floating potential is formed. This fact suggests that ion acceleration/heating iscaused by the steep potential gradient formed in the downstream by magnetized electrons.

c© 2013 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords: magnetic reconnection, spherical tokamak, plasma merging, two-fluid effect

DOI: 10.1585/pfr.8.2401130

1. IntroductionThe spherical tokamak (ST) is a promissing candidate

for core plasma confinement method of fusion reactor forthe following features.

• High-β value is achievable (∼50%).• Contain near-omnigenious region, which shows im-

proved confinement in bad curvature region [1].• Low cost in construction and operation.

However, because of the small aspect ratio (A < 2), therewould be no room for setting up center solenoid (CS) in-side the plasma. Therefore, many methods are being stud-ied to achieve CS-less startup of ST, such as the radio fre-quency (RF) startup, coaxial helicity injection (CHI) andmerging startup.

The merging startup uses the external poloidal field(PF) coils to form two ST plasmas without the CS. In merg-ing startup, two small tokamaks are formed and mergedto form one ST. During the ST formation, electrons andions are heated by an energy conversion process of mag-netic reconnection. This starup method has been usedfirstly by TS-3 (the University of Tokyo), then by START(UKAEA) [2] and recently by TS-4, MAST and UTST. 2DDoppler spectroscopy measured the ion temperature dur-ing merging startup in TS-3. In this experiment, ions areheated from 10 eV to 40 - 60 eV within 10 μsec, which cor-

author’s e-mail: [email protected]∗) This article is based on the presentation at the 22nd International TokiConference (ITC22).

responds to heating power of as large as 4 - 6 MW [3]. Inthe merging experiment in MAST, electron and ion temper-atures were measured by the Thomson scattering systemand neutral particle analyzer, respectively. They indicatethat both electrons and ions are heated up to 1 keV aftermerging. Precise electron temperature measurement wasalso implemented in MAST [4] and showed strong elec-tron heating at the X-point.

It is noted that the current sheet has higher ion temper-ature than the inflow region. Our experiment indicates thereconnection outflow as a the major heating mechanism,but needs a modification in the two-fluid regime. This pa-per addresses the first experimental observation of electro-static potential drop due to the two fluid effects and its heat-ing effect.

2. The UTST Plasma Merging DeviceThe merging startup ST device, UTST, is designed to

examine the feasibility of merging startup for fusion reac-tors. The cross-section of UTST is shown in Fig. 1. UnlikeSTART/MAST and TS-3/TS-4, all coils are placed outsidethe vacuum vessel. In the UTST merging startup exper-iment, PF#2,4 coil currents are swung to induce electricfield in toroidal direction for initial formation of two ST.After the initial tokamaks are formed, PF#1 coil currentcompress and merges them at the midplane of the vacuumvessel. With this startup method, we have produced suc-cessfully the maximum plasma current of 60 kA without

c© 2013 The Japan Society of PlasmaScience and Nuclear Fusion Research

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Fig. 1 Cross section diagram of UTST. Coil position, mag-netic probe distribution, and Ip Rogowski coil layout areshown. Line and color contours show poloidal flux andtoroidal current density of typical discharge calculatedfrom magnetic probe array signals.

Fig. 2 Time evolution of poloidal flux (line contour) withtoroidal current density (color contour) of typical dis-charge.

CS assist.The typical merging startup is shown in Fig. 2. Line

and color contour plot on Figs. 1 and 2 indicate poloidalflux ψ and toroidal current density jt, respectively. Thesevalues are calculated from the magnetic field measure-ment with a magnetic probe array placed inside the vac-uum vessel, as shown in Fig. 1. Magnetic probe array mea-sures toroidal and axial components of the magnetic field.Poloidal flux ψ, toroidal current density jt and toroidalelectric field Et are calcurated as follows,

ψ(R)=2π∫ R

0R′BzdR′, (1)

Et(R)= − 12πR

dψdt

∣∣∣∣∣R′=R, (2)

jt(R)= − 1μ0

[dBr

dz− dBz

dR′

]R′=R

= − 1μ0

[1

2πR′d2ψ

dz2− dBz

dR′

]R′=R

. (3)

3. Two-Fluid Effect On MagneticReconnectionMagnetic reconnection has been mainly described by

resistive MHD model. In this model, the diffusion by col-lisional resistivity is the cause for field-line reconnection.Since both of ion gyro-radius ρi ∼ 79 mm and the meanfree path λmfp ∼ 120 mm are longer than thickness of sheetcurrent δ ∼ 50 mm, ideal MHD interpretation of reconnec-tion needs some modification. In such a situation, elec-tron and ion must behave independently inside the currentsheet. The MHD interpretation of reconnection should bemodified by these effect such as Hall effect [5].

In this paper, we address the first experimental obser-vation of ion acceleration/heating caused by electron po-tential that magnetized electrons form during magnetic re-connection.

4. DiagnosticsTo see the two-fluid effect inside the current sheet, an

electrostatic probe was inserted to measure the radial pro-file of floating potential. The floating potential φf is a kindof electric potential where ion current and electron currentsbalance. φf is defined as follows;

φf = φs +κTe

e

[ln

(Zini

ne

√me

mi

)− 1

2

], (4)

where φs is the space potential Te is the electron temper-ature, Z is the ion charge number and ni,e are ion/electrondensity. As shown in eq. 4, φf is proportional to Te, thefloating potential difference can be, approximately, con-sidered as electrostatic potential difference, given that spa-tial difference of Te is sufficiently small. An ion Dopplerspectroscopy (IDS) probe was also inserted for ion veloc-ity/temperature measurement. Figure 3 shows these probelocations. The electrostatic probe is mainly composed ofφ10 mm glass tube with φ1 mm tungsten tip, which is in-serted into plasma by 5 mm. A linear isolation amplifier(ACPL-7900) is used to reduce the common mode noiseand insulation between the plasma and digitizer.

The IDS probe consists of optical lens and collimaterattached at the head of φ5 glass shaft with a quartz fiberinside it to gather and transmit ion emission to the detec-tor. In UTST, He II line (468.58 nm) emission localizedaround the X-point was already measured during magneticreconnection [6]. Since C III line (464.74 nm) emission isalso detected at almost the same time and location as theHe II line emission, C III line is used for ion flow velocityand temperature measurement.

We made a radial scan of this probe for measuring thespatial profiles of floating potential, ion flow velocity, and

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Fig. 3 Layout of electrostatic probe and IDS probe.

ion temperature.

5. Results and DiscussionFigure 4 shows r-z profiles of the poloidal flux and

toroidal current density and radial profile of the floatingpotential. Measurement area of the floating potential isshown as blue two-way arrow on line/color contour plot.

This figure indicates that the floating potential is uni-form across the current sheet at 200 μsec. After this timefloating potential suddenly form a steep gradient aroundR = 0.35 m, where the X-point is located around this time.The abrupt decrease of floating potential outside the X-point is due to charge non-neutrality just outside the X-point. This charge non-neutrality was caused by the differ-ence between the electron and ion motions around the X-point, indicating that the evidence of the two-fluid (Hall)effect during reconnection.

Time evolutions of reconnection rate (−(dψ/dt)) andtoroidal current density (− jt) at the X-point are shown inFig. 5. Also, radial profiles of floating potential (φf ) and ra-dial electric field (Er) at specific time are shown. From thisfigure, it can be noted that until 200 μs the reconnectionrate is no higher than the half of the peak reconnection rateand the toroidal current density continues growing up. Inthis phase, the floating potential is almost uniform and nosteepening appears and so radial electric field is almost uni-form across the current sheet. After 200 μs, the reconnec-tion rate rapidly grows up and come to its peak at 205 μs,on the other hand the toroidal current density decreases.We can see from this fugure that after 200 μs floating po-tential start to form a steep gradient around R = 0.35 m,i.e., around the X-point, and the radial electric field atR = 0.35 m suddenly starts to grow. The time evolutiontendency of these quantities can be paraphrased as follows:the two-fluid effect suddenly shows up when the reconnec-

Fig. 4 2D profile of poloidal flux (line contour) and toroidal cur-rent density (color contour) and radial profile of floatingpotential φf .

Fig. 5 Time evolutions of reconnection rate (−(dψ/dt)) andtoroidal current density (− jt) at X-point, and radial pro-files of floating potential (φf ) and radial electric field (Er)at t = 190, 200, 205 μsec.

tion rate abruptly grows up and the current density gradu-ally decreases. Also, this may indicate that two-fluid effectenhances reconnection rate.

Figure 6 shows the ion temperature at three radial po-sitions together with r-z contours of the poloidal flux andtoroidal current density, and the radial floating potentialprofile at 205 μs. Each signal from the IDS probe mea-surement is a line integrated emission from R = 0.1 m tothe measurement position, and each measurement regionof the IDS probe is denoted with black two-way arrowboth on contour plots of ψ and jt and radial profile plotof φf . From the IDS probe measurement data in Fig. 6, ra-dial flow as fast as Vi/VA ∼ 1 is detected at R = 0.36 m,0.46 m, where the X-point is included within the measure-ment area, while no ion flow is observed at R = 0.26 m,where the X-point is not included. The ion temperatureis much higher after the completion of the ST formation.The ion temperature measured at R = 0.26 m is higherthan that right after the ST formation but is still lower thanthat measured from the other positions. However, the fittedGaussian may contain the effect of bulk motions arond theX-point. There exist strong flow around and outside theX-point and also there may occur ion heating around theX-point.

The floating potential measurement indicates that the

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Fig. 6 The poloidal flux contour, floating potential profile andHeII line spectrums at three radial positions. The dashedline denote the center of the HeII line. The ion velocity isnormalized by the poloidal Alfvenspeed of 24 km/s.

potential drop outside the X-point accelerate ions, causingion heating around the X-point. In the UTST merging ex-periment, merging poloidal magnetic field Bp and toroidalmegnetic field Bt are typically 0.01 T and 0.1 T, respec-tively, therefore the C2+ gyration period is τCc = 3.9 μsand the gyroradius is ρC ∼ 16 mm. The acceleration timeis roughly calculated as follows: From the potential gra-dient calculation in Fig. 5, the electrostatic electric field isestimated as 400 < Er < 800 V/m. The acceleration timeτacc is calculated as follows.

τacc =Vimi

qEr, (5)

where Vi is the ion velocity Vi ∼ 27 km/s, q is the chargevalue of C2+, which is q = 3.2 × 10−19 C, mi is the massof C2+ so mi = 2.0 × 10−26 kg. Therefore, the accelerationtime τacc is 2.1 < τacc < 4.2 μs. The acceleration time canbe less than the gyration period of C2+, i.e., it is possiblefor C2+ to be accelerated up to 27 km/s only by the radialelectric field. The possible thermalization mechanisms for

accelerated ions are the remagnetization in the high-fielddownstream area and/or their collision in the downstreamarea with density pileup or fast shock [7]. Accelerated ionsare magnetized in the downstream region, converting ionflow energy to thermal energy. The downstream regionhas density pileup and/or fast shock. When the ions ac-celerated into this region, fast shock increases collisions,thermalizing ions.

6. ConclusionRadial profile of floating potential was measured for

the first time by the electrostatic probe during magnetic re-connection in the UTST. When the reconnection rate in-creases the sudden floating potential drop was observedoutside the X-point, as an evidence of two-fluid effect.This potential drop forms steep potential gradient aroundthe X-point, increasing the C2+ outflow to Vi/VA ∼ 1.This potential drop also causes ion heating around theX-point through some ion dumping mechanism. Thepossible dumping mechanisms are their remagnetizationand/or their collision in the downstream area with densitypileup/fast shock.

AcknowledgementsThis work was supported in partial by Grant-in-Aid

for Scientific Research (KAKENHI) 22246119, 22686085,25820434 and JSPS Core-to-Core Program 22001.

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Physics and 16th Intl. Congress on Plasma Physics, P1.013(Stockholm, Sweden, July 2–6, 2012).

[5] M. Yamada et al., Phys. Plasmas 13, 052119 (2006).[6] S. Kamio et al., IEEJ Trans. FM, Vol.132, No.1, in press

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Experimental Study of Two-Fluid Eﬀect during Magnetic